Aldous [1]} gave a rigorous proof of \(\zeta (2)\)  limit in the exponential case. His approach is based on the assignment analysis of an infinite tree with edges provided with exponentially distributed weights, see [2]}. In the same work he showed that the distribution \(\mathcal {P}\)  affects \(\lim _{n}{\mathbb {E}}\,{\min _{\pi } S(\pi )}\)  only through the value of its probability density function at 0, thus results for \(\mathcal {P} = U[0, 1]\)  and \(\mathcal {P} = \mathrm {Exp}(1)\)  are equivalent in asymptotic sense.
